Two metal spheres, one fo radius R and the other of radius 2R, both have same surface charge density s. They are brought in contact and seprated. What will be new surface charge densitites on them ?

Options

A. `5/2sigma, 5/4sigma`
B. `5/3sigma, 5/6sigma`
C. `3/5sigma, 6/5sigma`
D. `2/3sigma,1/2sigma`

Answer

B

Explanation

Before contant, changes of each sphere, ` q_(1) = sigma4piR^(2) ` and `q_(2) = sigma 4pi(2R)^(2) = 4 q_(1)`
When the two sphere are brought it contact ,their charges are shared till their potentials become equal i.e., `V_(1) + V_(2)`
`therefore " "(q_(1))/(4piepsi_(0)R) =(q_(2))/(4piepsi_(0)(2R))`
`therefore " " q_(2) = 2q_(1)" "...(i)`
As there is no loss of charge in the process
`therefore " " q_(1) + q_(2) = q_(1) + q_(2) = q_(1) + 4q_(1) = 5q_(1) = 5(sigma 4piR^(2))`
or `q_(1) + 2q_(1) = 5 sigma 4 piR^(2) " "("using (i)")`
`q_(1) = (5)/(3) sigma4piR^(2) and q_(2)= 2q_(1) = (10)/(3)(sigma 4 piR^(2))`
Hence `sigma_(1) = (q_(1))/(4piR^(2)) = (5)/(3) sigma, sigma_(2) = ( q_(2))/(4pi(2R)^(2)) = (5)/(6) sigma `